Question 132

Find the value of the expression $$x^{5}-12x^{4}+12x^{3}-12x^{2}+12x - 1$$ when $$x = 11$$.

Solution

Expression : $$x^{5}-12x^{4}+12x^{3}-12x^{2}+12x - 1$$

= $$x^5 + (-11x^4 - x^4) + (11x^3 + x^3) + (-11x^2 - x^2) + (11x + x) - 1$$

= $$(x^5 - 11x^4) + (11x^3 - x^4) + (x^3 - 11x^2) + (11x - x^2) + (x - 1)$$

= $$x^4(x - 11) + x^3(11 - x) + x^2(x - 11) + x(11 - x) + (x - 1)$$

Putting $$x = 11$$

= 11 - 1 = 10

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